For centuries, rotating masses have been used both to store kinetic energy for future use and to provide a smoother output of energy from installations in which the energy input is intermittent or changes abruptly. In recent years, the production, conservation, and storage of energy obtained from fossil fuels have become problems of global concern. The concern has led to a more concerted effort to evaluate the ultimate potential of rotating masses, particularly flywheels, as energy storage devices. Benefitting the recently intensified interest in rotating masses or flywheels as energy storage devices is the development of new structural materials that offer advantages over materials previously utilized in flywheels. Materials such as glass fibers, carbon fibers, and aramid fibers all have specific strengths, or ratios of strength to density, that are greater than the specific strength of high strength steel, for example. As will be explained, a material that has a high ratio of strength to density offers the possibility of a high energy storage capacity for a flywheel that is fabricated of such a material.
To understand the importance to flywheels of the high specific strengths of recently developed filamentary materials, consideration must be given to the factors that control energy storage capacity. The critical factors can be understood by considering a flywheel of circular shape and uniform thickness throughout which is fabricated of an isotropic material, such as steel. Isotropic materials, which have equal properties (e.g., strength) in all directions, are to be distinguished from anisotropic materials, such as the high strength filamentary materials mentioned above, which have different properties in different directions. The kinetic energy (E.sub.K) that is stored in an isotropic rotating flywheel is determined by the following equation: EQU E.sub.K =1/2I.omega..sup.2. (1)
In equation (1), .omega. is the rotational velocity of the flywheel in radians per second and I is the moment of inertia of the flywheel in kilogram-meters squared. The moment of inertia (I) of the disc-shaped flywheel is, in turn, defined by the equation: EQU I=1/2mr.sup.2. (2)
In equation (2), m is the mass of the flywheel in kilograms, while r is its radius in meters. From equations (1) and (2), it can be seen that the energy stored in a flywheel may be increased by increasing any one of the following factors: mass, radius, and rotational velocity. Since the radius and rotational velocity factors are squared in determining the kinetic energy stored in the flywheel, increasing the radius and/or the rotational velocity of a flywheel is a more efficient and effective method of increasing energy storage capacity than increasing the mass of the flywheel.
The maximum kinetic energy that may be stored in a flywheel is limited by the strength of the material of which the flywheel is fabricated. The strength of the material is used to resist the radial and tangential or circumferential stresses that result from the centrifugal loads imposed on the flywheel as it is rotated. The maximum radial and tangential stresses (.sigma..sub.r,.sigma..sub..theta.) in a solid, isotropic flywheel both occur at the center of the flywheel and are equal to each other. The stresses are determined by the following equation: EQU .sigma..sub.r =.sigma..sub..theta. =1/8.rho..omega..sup.2 /386.4(3+.nu.)r.sup.2. (3)
In equation (3), .rho. is the density of the flywheel material in pounds per cubic inch and .nu. is Poisson's ratio for the flywheel material. By comparing equations (1) and (2) with equation (3), it can be seen that the factors that tend to increase the amount of energy stored in a flywheel contribute in the same degree to the radial and tangential stresses in the flywheel. Consequently, the maximum theoretical energy storage capacity of a flat, solid (i.e., no openings), disc-shaped flywheel can only be increased by fabricating the flywheel of a higher strength material. The increase in material strength must be achieved, however, without an increase in density because density is a factor that directly affects the radial and tangential stresses. Thus, a high ratio of strength to density is an important chracteristic of a preferred flywheel material. The specific strength or strength to density ratio is critical regardless of the shape of the flywheel.
Because of the importance of the specific strength of the material of which a flywheel is fabricated, many efforts have been made to incorporate recently developed, high strength, anistropic filamentary materials into flywheels. In one type of flywheel that utilizes anisotropic filamentary materials, the filaments are circumferentially wound about a central hub, and an axis of rotation, to produce a circular flywheel. In another type of filamentary flywheel, the filaments are disposed normal to the axis of rotation of the flywheel. When disposed normal to the axis of rotation, the filaments may be individually secured to a central hub or they may be bonded together in a matrix material to form a solid or continuous member. A third type of filamentary flywheel incorporates short (e.g., chopped) anisotropic filaments randomly dispersed in a resin matrix that is molded to a desired shape. Substantial work in the field of filamentary flywheels has been done by David Rabenhorst of the Applied Physics Laboratory at The Johns Hopkins University. Mr. Rabenhorst is the inventor or coinventor of several patented flywheel designs employing filamentary materials. Mr. Rabenhorst's patented flywheels are described and illustrated in patents such as: Rabenhorst U.S. Pat. No. 3,672,241; Rabenhorst U.S. Pat. No. 3,698,262; Rabenhorst U.S. Pat. No. 3,737,694; Rabenhorst et al U.S. Pat. No. 3,788,162; Rabenhorst U.S. Pat. No. 3,884,093; Rabenhorst U.S. Pat. No. 3,964,341; Rabenhorst U.S. Pat. No. 3,982,447; Rabenhorst U.S. Pat. No. 4,000,665; Rabenhorst U.S. Pat. No. 4,020,714; and Rabenhorst U.S. Pat. No. 4,023,437. Other flywheels or rotary energy storage devices that utilize high strength filaments are described and illustrated in patents such as: Reinhart, Jr. U.S. Pat. No. 3,296,886; Wetherbee, Jr. U.S. Pat. No. 3,602,066; Wetherbee, Jr. U.S. Pat. No. 3,602,067; Post U.S. Pat. No. 3,683,216; Post U.S. Pat. No. 3,741,034; and Post U.S. Pat. No. 3,859,868.
As previously mentioned, the strength, tensile modulus, and other properties of anisotropic, filamentary materials are significantly greater in one direction, typically along the length of the filaments, than in other directions. Consequently, flywheel designs that incorporate anisotropic, filamentary materials attempt to orient the filaments such that they are stressed primarily in the direction of their greatest strength. Ideally, a filamentary flywheel should also be designed such that, at its operating speed, all of the filaments are stressed to or near their ultimate strengths all along their lengths. As a practical matter, however, a flywheel in which all filaments are stressed to their limits is not possible. The closest approximation to such an ideal flywheel is a flywheel that consists primarily of a thin rim of filaments that are wound so as to encircle their axis of rotation at some finite radial distance. The primary stresses imposed on the filaments will be oriented along their lengths and will increase in proportion to the square of the radial distance of the filaments from the axis of rotation. With a sufficiently thin rim, the variation in stresses from the inner circumference of the rim to the outer circumference of the rim can be minimized. Although a thin rim flywheel is very efficient in terms of energy density or energy stored per unit weight, the flywheel is equally inefficient when viewed in terms of energy stored per unit of volume enclosed or swept out by the flywheel as it rotates.
To provide flywheels that are more efficient, from a volumetric standpoint, than the thin rim, wound filament flywheel, some researchers have turned to filling in the volume between a thin rim and its axis of rotation. The usual approach to "filling in" a thin rim flywheel is to provide additional windings of filaments that are disposed closer to the axis of rotation than the rim. If all of the filamentary windings are fabricated of the same material, the windings closer to the axis of rotation are less heavily stressed and contribute less to the energy storage capacity of the flywheel than the filaments adjacent the outer circumference of the flywheel. More importantly, however, since strain is proportional to stress, the radially outermost circumferential filaments expand or stretch more than the inner circumferential filaments and cause the flywheel to break into many concentric rings long before any of the filaments reach their breaking stress. To overcome the problem of having a wound filamentary flywheel break into concentric rings, it has been proposed to increase the modulus of elasticity of such a wound flywheel with increasing radial distance from the axis of rotation. Thus, although the filaments located closer to the axis of rotation will not be as highly stressed as the filaments closer to the outer circumference of the flywheel, the radially inner filaments will expand or stretch more easily and under less load than the radially outer filaments and will be able to keep pace with the outward expansion of the outermost filaments. Flywheels that incorporate such a principle are described and illustrated in Reinhart, Jr. U.S. Pat. No. 3,296,886, Wetherbee, Jr. U.S. Pat. No. 3,602,066, and Wetherbee, Jr. U.S. Pat. No. 3,602,067. More recently, it has been proposed, in Rabenhorst U.S. Pat. Nos. 3,964,341 and 4,020,714, to tie together adjacent filaments or groups of filaments at discrete and separate points about the circumference of a wound filament flywheel. Between the tie points, the filaments are free to stretch at any rate determined by the rotational speed of the flywheel and the radial position of the filaments.
Efforts to improve the volumetric efficiency of filamentary flywheels, in comparison to thin rim, wound flywheels, have also included the design of flywheels in which the filaments are oriented other than circumferentially of the axis of rotation. As shown in Rabenhorst et al U.S. Pat. No. 3,788,162, a filamentary flywheel may be fabricated of a plurality of parallel plies or plates of parallel, anisotropic filaments embedded in a resin matrix. The plies are bonded together to form a disc-shaped rotor that rotates about an axis disposed perpendicular to the plies of filamentary material. In such a flywheel, anisotropic filaments that pass through or close to the axis of rotation will be stressed primarily along their lengths and will experience maximum stresses at their longitudinal centers. Filaments that do not pass through or close to the axis of rotation, however, will not be as highly stressed along their lengths and will also be subject to unbalanced radial and tangential loads that will tend to force the filaments out of the resin matrix and the flywheel. Another flywheel construction shown in the Rabenhorst et al patent is the use of short filaments randomly dispersed in a resin matrix. Because of their random orientation, very few of the filaments are correctly oriented so as to be stressed to their maximum or ultimate strengths. Nonetheless, such as flywheel is inexpensive to fabricate, in comparison to wound filament flywheels and flywheels fabricated of laminated sheets or plies. It also offers reasonably good volumetric efficiencies. In terms of its efficiency per unit weight, a flywheel fabricated of randomly oriented filaments may offer energy storage capacities on the order of two to ten watt-hours per pound.